Constructing sequences with high nonlinear complexity using the Weierstrass semigroup of a pair of distinct points of a Hermitian curve

Hans Olav Geil, Ferruh Ozbudak, Diego Ruano Benito

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

Resumé

Using the Weierstrass semigroup of a pair of distinct points of a Hermitian curve over a finite field, we construct sequences with improved high nonlinear complexity. In particular we improve the bound obtained in Niederreiter and Xing (IEEE Trans Inf Theory 60(10):6696–6701, 2014, Theorem 3) considerably and the bound in Niederreiter and Xing (2014, Theorem 4) for some parameters.
OriginalsprogEngelsk
TidsskriftSemigroup Forum
Antal sider13
ISSN0037-1912
DOI
StatusAccepteret/In press - 1 jan. 2018

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Hermitian Curve
Semigroup
Distinct
Theorem
Galois field

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abstract = "Using the Weierstrass semigroup of a pair of distinct points of a Hermitian curve over a finite field, we construct sequences with improved high nonlinear complexity. In particular we improve the bound obtained in Niederreiter and Xing (IEEE Trans Inf Theory 60(10):6696–6701, 2014, Theorem 3) considerably and the bound in Niederreiter and Xing (2014, Theorem 4) for some parameters.",
keywords = "Weierstrass semigroup, Weierstrass pair, Hermitian function field, Sequences, Nonlinear complexity",
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Constructing sequences with high nonlinear complexity using the Weierstrass semigroup of a pair of distinct points of a Hermitian curve. / Geil, Hans Olav; Ozbudak, Ferruh; Ruano Benito, Diego.

I: Semigroup Forum, 01.01.2018.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

TY - JOUR

T1 - Constructing sequences with high nonlinear complexity using the Weierstrass semigroup of a pair of distinct points of a Hermitian curve

AU - Geil, Hans Olav

AU - Ozbudak, Ferruh

AU - Ruano Benito, Diego

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Using the Weierstrass semigroup of a pair of distinct points of a Hermitian curve over a finite field, we construct sequences with improved high nonlinear complexity. In particular we improve the bound obtained in Niederreiter and Xing (IEEE Trans Inf Theory 60(10):6696–6701, 2014, Theorem 3) considerably and the bound in Niederreiter and Xing (2014, Theorem 4) for some parameters.

AB - Using the Weierstrass semigroup of a pair of distinct points of a Hermitian curve over a finite field, we construct sequences with improved high nonlinear complexity. In particular we improve the bound obtained in Niederreiter and Xing (IEEE Trans Inf Theory 60(10):6696–6701, 2014, Theorem 3) considerably and the bound in Niederreiter and Xing (2014, Theorem 4) for some parameters.

KW - Weierstrass semigroup

KW - Weierstrass pair

KW - Hermitian function field

KW - Sequences

KW - Nonlinear complexity

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U2 - 10.1007/s00233-018-9976-8

DO - 10.1007/s00233-018-9976-8

M3 - Journal article

JO - Semigroup Forum

JF - Semigroup Forum

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